Add the blackberries and lemon juice to a large 8-quart pot. Set over medium heat and bring to a boil. Reduce the heat and let the mixture simmer for 2 to 3 minutes.
While the berries are simmering, slice off the stems of the jalapeños, cut them in half lengthwise, and remove the seeds and membranes if desired. Finely mince the peppers.
Mash the softened blackberries in the pot using a potato masher or the back of a spoon. Leave some texture or mash to a smoother consistency, depending on preference.
Stir in the sugar and minced jalapeños. Mix until the sugar begins to dissolve.
Raise the heat to medium-high and bring the mixture to a rolling boil. Let it boil uncovered for 20 to 30 minutes, stirring often to prevent sticking.
Check for doneness by using a candy thermometer—the jam should reach 220°F. Alternatively, spoon a little jam onto a cold plate, wait a few seconds, and run a finger through it. If the line holds and doesn’t run back together, it’s ready.
Remove from heat and skim off any foam that may have collected on top. Let the jam rest for 5 to 10 minutes before filling jars.
Ladle hot jam into clean jars, leaving ¼ inch of headspace.
If canning, transfer the hot jam into sterilized jars, wipe the rims, apply the lids, and process in a boiling water bath canner for 10 minutes (adjust for altitude if needed). Carefully remove the jars and let them cool undisturbed on a towel for 12 to 24 hours. Check that the lids have sealed before storing. Properly canned jars can be stored in a cool, dark place for up to 1 year.
If skipping canning, allow the jars to cool completely at room temperature. Once cool, store in the refrigerator for up to 1 month or in the freezer for up to 6 months. If freezing, leave a little headspace to allow for expansion.